In this paper, we try to demonstrate a method to generate new class of exact solutions to the Einstein’s field equations (EFE) by introducing a new parameter (κ) in the Vaidya–Tikekar metric ansatz describing a static spherically symmetric relativistic star having anisotropic fluid pressure. We particularly obtained solutions in closed form in terms of trigonometric functions. Introduction of a new parameter in the metric ansatz predicts some interesting results. In our formalism, the main feature of the new class of solutions is that one can study the effects of the new parameter (κ) on different physical parameters of a compact object such as its mass, radius, surface redshift etc. Moreover, if we switch off the new parameter (κ = 0), it also gives new realistic solutions which arethe modified version of isotropic Matese–Whitman solutions in the presence of pressure anisotropy. Consequently, we present here that a plethora of well-known stellar solutions can be identified as sub-class (κ = ±1) of ourclass of solutions. We predict here the maximum mass of compact object in isotropic case and also in the presence of pressure anisotropy. The central density is found to be as high as ∼10$^{15}$ gm/cc and thus the present model is capable enough to accommodate a wider class of compact objects. We examine the physical viability of solutions for studying relativistic compact stars and it is found that all the stability conditions are satisfied.

In this article, we have studied the solutions of Einstein–Maxwell field equations for compact objects in the presence of net electric charge. Interior physical 3-space is defined by Vaidya–Tikekar metric in spheroidal geometry. The metric is characterised by two parameters, namely, spheroidal parameter K and curvature parameter R. The nature of the interior fluid is considered to be anisotropic. Assuming strange matter equation of state (EOS)in the MIT Bag model for the interior matter content, namely, p = $\frac{1}{3}$(ρ − 4 B), where B is the Bag constant, we determine various physical properties of the charged compact star. We have taken the value of surface density ρs(= 4 B) as a probe to evaluate the mass–radius relation for the compact star in the presence of net electric charge and using the range of B necessary for possible stable strange matter. It is interesting to note that in this model thereexist a maximum radius of a star which depends on B. We further note that compactness of the star corresponding to the maximum radius always lies below the Buchdahl limit ($\le$$\frac{4}{9}$) for the maximum allowed value of the pressure anisotropy and electromagnetic field. Energy and causality conditions hold good throughout the star in the presence of charge also. Prediction of mass of the strange stars is possible in the present model. We have determined mass, radius, surface red-shift and other relevant physical parameters of the compact objects.